Homework Statement
Solve 2^{k-2}=3^{k+1}
Homework Equations
The Attempt at a Solution
2^{k-2}=3^{k+1}
\frac{2^{k}}{2^{2}}=(3^k)(3^1)
\frac{2^{k}}{3^{k}} = 4 \cdot 3
\frac{2^{k}}{3^{k}} = 12
What do I do next to solve for K?
Homework Statement
For the function f(x) = 3sin 2x, find the instantaneous rate of change at point A (\frac{\pi}{6}, f(\frac{\pi}{6}))
Homework Equations
iroc = instantaneous rate of change
iroc= \lim_{h\to 0} \frac{f(a+h) - f(a)}{h}
The Attempt at a Solution
iroc = instantaneous...
Ok so after I fix the silly mistake, this is how far I get.
iroc= \lim_{h\to 0} \frac{(\frac{-20.4h-40.8}{h^2 + 4h +40} + 6.5) - 5.48}{h}
iroc= \lim_{h\to 0} \frac{(\frac{-1.02^2 - 24.48h-81.6}{h^2 + 4h +40})}{h}
I'm not sure what I should do next.
Homework Statement
After you eat something that contains sugar, the pH level in our mouth changes. This can be modeled by the function L(m)=(\frac{-20.4m}{m^2 + 36}) + 6.5 where L is the pH level and m is the number of minutes that have elapsed since eating. Find the instantaneous rate of...
So it's my last year in high school and I enjoy programming but I don't know if I should apply to either computer science or software engineering. What really is the difference between the two majors?
Homework Statement
Your favourite physics teacher who is late for class attempts to swing from the roof of a 24-m high building to the bottom of an identical building using a 24m rope as shown in Figure 5. She starts from rest with the rope horizontal, but the rope will break if the tension...
Homework Statement
Kepler's third law of planetary motion relates P, the period of a planet's orbit, to R, the planet's mean distance from the sun, through the equation log P = \frac{1}{2} (log K + 3log R), where K is a constant.
Rewrite the formula as a single logarithm.
Homework...
Homework Statement
Given the exponential function and its inverse, where a > 0
Exponential Function:
f(x)=a^x
Inverse function:
f^{-1}(x)=log_ax
a) For what values of a do the graphs of f(x)=a^x and f^(-1)(x) intersect?The Attempt at a Solution
I have no idea how to start this question.
Off...
Homework Statement
A 25.6-kg boy pulls a 4.81-kg toboggan up a hill inclined at 25.7º to the horizontal. The vertical height of the hill is 27.3 m and the coefficient of friction of the hill surface is 0.4
a) Determine how much work the boy must apply on the toboggan to pull it at a constant...